(Reuters) - T.J. Rodgers, chief executive of Cypress Semiconductor Corp., had a simple solution to the hassles of getting visas for foreign engineers he needed to run his $1 billion business.

"When I hire an Indian PhD today, I hire him in Bangalore, not San Jose. Now I can hire all I want and not have to worry about the vagaries of government decrees," Rodgers said.

"They've made it less tenable to do business here, so we do business elsewhere," Rodgers told Reuters in an interview.

News this week that the U.S. immigration service hit its annual quota for skilled worker visas in one day highlighted what Rodgers and other executives said is the need for reform of a system overwhelmed by New Economy hiring demands.

On Monday, the first day people could apply for the next round of H-1B visas that allow skilled foreigners to work in the United States, authorities were flooded with a record number of applications -- more than 150,000.

The government plans to grant 65,000 H-1B visas to those who hold the equivalent of an undergraduate degree and have expertise in a specialized field. Another 20,000 visas will go to people with advanced degrees.

Executives say the chronic shortage of American engineers, programmers and scientists is forcing many companies to expand overseas, while also squeezing smaller companies that do not have the money for such expansion.

"The problem, obviously, is that not every company has that ability to relocate people overseas," said Robert Hoffman, vice president of government affairs for business software maker Oracle Corp..

"A lot of small companies rely on H-1Bs. A lot of companies were started by those who were here on H-1Bs," said Hoffman, who is also co-chair of Compete America, an industry group that advocates easier rules on foreign workers.